RATIOS and

PROPORTIONS


Solving Proportions

Proportions can be Solved when Three of the Four parts of the

Proportion are known.




Solving for an Unknown

When one value is unknown, that value is assigned a letter. Most

commonly that letter is X.



A Proportion with one unknown.


3
:
4
::
X
:
8





Solving for X



(1) Find the Means and the Extremes.


3
:
4
::
X
:
8
4 and X are the means


3
:
4
::
X
:
8
3 and 8 are the extremes



(2) Multiply the extremes and place the product to the left

of the equal sign.


3
:
4
::
X
:
8
24 = 4X



(3) Multiply the means and place the product to the right

of the equal sign.


3
:
4
::
X
:
8
24 = 4X



(3) Solve for X by dividing the number opposite the equal

sign by the number on the same side as the equal sign.


24 4 = X


6 = X


3
:
4
::
6
:
8





More Examples of Solving Proportions



3
:
10
::
6
:
X


3X = 60


X = 60 3


X = 20


3
:
10
::
6
:
20



* * * * *



5
:
15
::
X
:
3


15 = 15X


15 15 = X


1 = X


5
:
15
::
1
:
3



* * * * *



2
:
7
::
8
:
X


2X = 56


X = 56 2


X = 28


2
:
7
::
8
:
28